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The perimeter of a rectangular traffic sign is 106 inches. Also its length is 15 inches longer than its width. What is the length and the width of this sign?

Guest Mar 6, 2015

Best Answer 

 #1
avatar+19207 
+5

The perimeter of a rectangular traffic sign is 106 inches. Also its length is 15 inches longer than its width. What is the length and the width of this sign ?

Let L = length and W = width

perimeter :  106 = 2L + 2W     (1)

L = W + 15

L-W = 15  | *2

2L - 2W = 30      (2)

$$\\(1) \qquad 2L + 2W = 106 \\
(2) \qquad 2L - 2W = 30$$

$$\begin{array}{lrcl}
\hline
(1)+(2):& 4L &=& 136\\\\
& L &=& \dfrac{136}{4} \\\\
& \textcolor[rgb]{1,0,0}{L} & \textcolor[rgb]{1,0,0}{=} & \textcolor[rgb]{1,0,0}{34} } \\\\
\hline
& W &=& L - 15 \\\\
& W &=& 34 - 15 \\\\
& \textcolor[rgb]{1,0,0}{W} & \textcolor[rgb]{1,0,0}{=} & \textcolor[rgb]{1,0,0}{19} }
\end{array}$$

heureka  Mar 6, 2015
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1+0 Answers

 #1
avatar+19207 
+5
Best Answer

The perimeter of a rectangular traffic sign is 106 inches. Also its length is 15 inches longer than its width. What is the length and the width of this sign ?

Let L = length and W = width

perimeter :  106 = 2L + 2W     (1)

L = W + 15

L-W = 15  | *2

2L - 2W = 30      (2)

$$\\(1) \qquad 2L + 2W = 106 \\
(2) \qquad 2L - 2W = 30$$

$$\begin{array}{lrcl}
\hline
(1)+(2):& 4L &=& 136\\\\
& L &=& \dfrac{136}{4} \\\\
& \textcolor[rgb]{1,0,0}{L} & \textcolor[rgb]{1,0,0}{=} & \textcolor[rgb]{1,0,0}{34} } \\\\
\hline
& W &=& L - 15 \\\\
& W &=& 34 - 15 \\\\
& \textcolor[rgb]{1,0,0}{W} & \textcolor[rgb]{1,0,0}{=} & \textcolor[rgb]{1,0,0}{19} }
\end{array}$$

heureka  Mar 6, 2015

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